Nash led the way for the Rangers with the game-tying goal in the opening minute of the third, and assisted on Vesey's game-winner with just over five minutes to play.
After surrendering two first period goals, Henrik Lundqvist was solid the rest of the way and finished the night with 26 saves for his 11th win of the season, and his 10th straight victory over the Hurricanes at The Garden.
The Rangers took two of three games against the Sabres last season, including the lone contest in western New York, tallying three or more goals in each of the three games. Mats Zuccarello led the way offensively with two goals and two assists, while Jesper Fast had a goal and three helpers.
If he gets the start, Lundqvist is 17-10-2 with a 2.29 GAA and a .919 SV% with two shutouts lifetime against the Sabres. In his last seven appearances against Buffalo, Lundqvist is 6-0 with a 2.05 GAA and a .923 SV% with one shutout.
Backup Antti Raanta is 1-1 against Buffalo, with his most recent appearance coming last season in a 4-2 win over the Sabres in Buffalo on March 8.
The Sabres enter tonight's game 5-5-2 in their last 10 and are currently second to last in the Eastern Conference with 21 points.
The good news, though, is that rising star Jack Eichel returned to the lineup Tuesday night in a 5-4 win over the Ottawa Senators and quickly made his presence known with a goal and an assist in 17:08 of ice time.
Former Islander Kyle Okposo is off to a strong start in his first year with the club, posting a team-high seven goals and eight assists for 15 points through 21 games. Ryan O'Reilly is second on the team with six goals and six assists for 12 points in 16 contests.
Goaltender Robin Lehner is 5-7-3 with a 2.40 GAA and a .921 SV% in 16 games this year. Backup Anders Nilsson is 3-2-2 with a 2.20 GAA and a .939 SV % with one shutout in seven games (six starts).
Buffalo has the fifth-best power play in the NHL at 22.7%, though its penalty kill has struggled with a success rate of just 78.7%, sixth-worst in the League.
